Numerical Program Optimization for High-Level Synthesis

Abstract

This paper introduces a new technique, and its associated open source tool, SOAP2, to automatically perform sourceto-source optimization of numerical programs, specifically targeting the trade-off between numerical accuracy and resource usage as a high-level synthesis flow for FPGA implementations. We introduce a new intermediate representation, which we call metasemantic intermediate representation (MIR), to enable the abstraction and optimization of numerical programs. We efficiently discover equivalent structures in MIRs by exploiting the rules of real arithmetic, such as associativity and distributivity, and rules that allow control flow restructuring, and produce Pareto frontiers of equivalent programs that trades off LUTs, DSPs and accuracy. Additionally, we further broaden the Pareto frontier in our optimization flow to automatically explore the numerical implications of partial loop unrolling and loop splitting. In real applications, our tool discovers a wide range of Pareto optimal options, and the most accurate one improves the accuracy of numerical programs by up to 65%.

Automatically Optimizing the Latency, Area, and Accuracy of C Programs for High-Level Synthesis

“…1 equivalent expressions [6,7]. We therefore base our optimizer on the open-source SOAP2 framework [6,8], which specifically tackles the efficient discovery of equivalent structures in numerical programs, by intelligently pruning the set of candidates as it progresses up the input program's abstract syntax tree. We also exploit SOAP2's ability to analyze the numerical accuracy of a given program.…”

“…Following Gao et al, we therefore perform transformations not on the program text directly, but on a DAG representation of the program called a MIR [8]. It expresses how each program variable is updated, but abstracts away the order in which the updates occur, and ignores any temporary variables that are not marked as program outputs.…”

“…MIRs are also capable of representing loops [8], but we do not exploit that in this paper, despite the centrality of loops to our work. When we optimize loop nests, we are specifically applying transformations to the kernels of the flattened loop nests.…”

“…Gao et al [8] did not include support for arrays in their original description of the MIR format. However, the examples that motivate our work all include arrays, so in this paper, we extend MIRs to be able to represent programs that use single-or multi-dimensional arrays.…”

“…To tackle Table 2: Before-and-after examples to demonstrate the transformation rules we used. The arithmetic and control flow rules are inherited from Gao et al [8]; the access reduction rules are introduced in this work.…”